A number of attempts have been made to accurately determine shear stress under turbulent flow conditions. These include the use of flush-mounted film gages and hot wires mounted in a number of locations including embedded in the surface to be tested or above that surface. It has been found that difficulties were encountered in calibrating these prior gages, so that in general they could not provide accurate readings of skin-friction in turbulent flows. The measurement of skin-friction in air by means of heated elements, surface gages or hot wires or films close to the wall is the subject of considerable research. Most of the previous work is concerned with the determination of mean skin-friction.
It is common knowledge that large fluctuations in skin-friction occur in turbulent flows. A relatively standard practice has been to calibrate instruments in a laminar flow of known characteristics and then apply the calibration results to sensor output in a turbulent flow to obtain shear stress readings. However, this procedure is known to be generally inaccurate when applied to many types of skin-friction gages. The assumption of the applicability of the laminar flow calibration to turbulent flow gives incorrect answers for skin-friction. As a matter of fact, for some types of prior art probes it has been found that the calibration of the probes in laminar flow cannot be used to obtain even the mean shear stress in a turbulent flow. Other studies have shown that the correct results for mean shear can be obtained only when a pseudo-calibration is performed. In this technique, which is termed a "turbulent calibration," the mean sensor output is determined when the mean skin friction is known, for example, when the probe is mounted in turbulent channel flow so that the mean pressure gradient determines the mean wall shear. The resulting calibration curve is interpreted in terms of the mean skin-friction. This procedure has significant limitations. It provides a method for obtaining mean data only in turbulent flows with a similar turbulent structure and is widely used therefor, but it is not generally satisfactory for obtaining accurate time-resolved skin-friction data.
An important difficulty in application of a laminar flow calibration to the measurement of either the mean or the time resolved skin-friction, relates to the temperature distribution in the wall in the immediate vicinity of the sensor and to the influence of that distribution on the sensor output. The extent of that influence depends on the thermal properties of the wall and on the detailed design of the gage. This difficulty has several manifestations. One of them is that the response of the wall to the spectrum of fluctuations in wall shear in a turbulent flow results in a mean temperature distribution in the wall which can differ from that in a laminar flow with a shear stress equal to the mean turbulent shear. This influence of the thermal field in the wall on the sensor is evident from testing which shows that in a laminar flow the effect of the wall on the output of a hot wire can be represented by a constant heat loss independent of the shear. In a turbulent flow, with the wire mounted sufficiently close to the wall so that it is within the viscous sublayer, it appears that the heat loss to the wall for a given mean shear is different from that measured in a laminar flow at that same shear. This result is consistent with the fact that the determination of even mean skin-friction in turbulent flows requires a "turbulent calibration," as mentioned above.
A second manifestation of the influence of wall temperature on sensor output relates to the interaction between the thermal field of the sensor and the linear velocity profile prevailing near the wall in laminar flow and in the viscous sublayer in a turbulent flow. When hot wire/films are used as skin-friction gases, they must be sufficiently close to the wall so that for the maximum shear stress to be measured they are well within the viscous sublayer.
Another manifestation of the influence of the wall on sensor output is the relatively long response time of the wall temperature to changes in heat transfer as a consequence of changes in wall shear. The combination of sensor and wall must be considered a single unit insofar as frequency response is concerned. The consequent degraded frequency response of gages using flush-mounted films and embedded wires makes them difficult to apply for time-resolved measurements. If by proper design the extent of the thermal field in the wall surrounding such sensors is made suitably small, laminar calibration of these gages can lead to accurate measurements of the mean turbulent shear stress, but this feature alone does not assure accuracy of time resolved data.
It has long been known to embed a hot wire in a plug of low thermal diffusivity for the measurement of mean shear stress. It is argued that the use of a material with such a property reduces the heat loss to the surrounding wall and thus the influence of the temperature field in the wall on the sensor output as well. Another alternative in this general structure is to employ an air gap between a flush-mounted film and the surrounding wall.
In the calculations required for calibrating a skin-friction instrument, it has been found that it is necessary to determine a fictitious length L associated with a particular gage operated under particular conditions. This length is defined as the length of wall on which a constant wall temperature would reproduce the actual heat loss associated with the distributed wall temperature. The length L can be considerably greater than either the streamwise dimension of a film or the diameter of a wire/film adjacent to the wall. It appears that one criterion for obtaining from a laminar calibration the correct mean turbulent shear stress is that the effective length of the gage be small.
Relatively little quantitative information is available concerning the frequency response characteristics of skin-friction gages. There is evidence to show that flush-mounted films possess complex low frequency characteristics due to their thermal interaction with the supporting substrate. It appears that certain of the flush-mounted gage structures have small effective lengths. A gage with a small effective length mounted in a material with a small thermal diffusivity may have an adequate frequency response but sufficient information is not available.
In skin-friction gages comprising hot wires/films mounted close to the wall, heat transfer from the sensor to the wall leads to altered sensor output and to failure of a laminar calibration to provide accurate mean turbulent shear stress. However, it appears that the frequency response of such gages is not seriously degraded by the interaction of wall and sensor.